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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Evaluating and Quantifying the Climate-Driven Interannual Variability in Global Inventory Modeling and Mapping Studies (GIMMS) Normalized Difference Vegetation Index (NDVI3g) at Global Scales

Satellite observations of surface reflected solar radiation contain informationabout variability in the absorption of solar radiation by vegetation. Understanding thecauses of variability is important for models that use these data to drive land surface fluxesor for benchmarking prognostic vegetation models. Here we evaluated the interannualvariability in the new 30.5-year long global satellite-derived surface reflectance index data,Global Inventory Modeling and Mapping Studies normalized difference vegetation index(GIMMS NDVI3g). Pearsons correlation and multiple linear stepwise regression analyseswere applied to quantify the NDVI interannual variability driven by climate anomalies, andto evaluate the effects of potential interference (snow, aerosols and clouds) on the NDVIsignal. We found ecologically plausible strong controls on NDVI variability by antecedent precipitation and current monthly temperature with distinct spatial patterns. Precipitation correlations were strongest for temperate to tropical water limited herbaceous systemswhere in some regions and seasons 40 of the NDVI variance could be explained byprecipitation anomalies. Temperature correlations were strongest in northern mid- to-high-latitudes in the spring and early summer where up to 70 of the NDVI variance was explained by temperature anomalies. We find that, in western and central North America,winter-spring precipitation determines early summer growth while more recent precipitation controls NDVI variability in late summer. In contrast, current or prior wetseason precipitation anomalies were correlated with all months of NDVI in sub-tropical herbaceous vegetation. Snow, aerosols and clouds as well as unexplained phenomena still account for part of the NDVI variance despite corrections. Nevertheless, this study demonstrates that GIMMS NDVI3g represents real responses of vegetation to climate variability that are useful for global models.

interference↗
DOE OSTI2020

Verification of Special Nuclear Material (SNM) using Active Well Coincidence Counter (AWCC) and a High Purity Germanium (HPGe) Detector

SNM verification can be accomplished via two methods i.e. destructive analysis (DA) or nondestructive analysis (NDA). The DA modes are much more accurate compared to NDA modes; nevertheless, the sample's physical integrity is destroyed in the process. Techniques such as ICP-MS, ID-ICP-MS, TI-MS are few examples of DA, where a bulk material is ground and mixed with a solution (some form of acid) to acquire a homogenous sample. In contrast, NDA modes utilize signals emitted by the sample such as gamma, neutrons, light, or heat to analyze samples under investigation. HPGe detectors are some of the most frequently used gamma detectors to assay SNM. However, in a high activity scenario it provides a large uncertainty and sometimes becomes unfeasible to measure low energy gamma rays. Meanwhile, neutron detectors are not affected by the gamma background, therefore they can be used in addition to the gamma detectors to verify total fissile mass ({sup 235}U + {sup 239}Pu) of SNM. The AWCC is one of the thermal neutron NDA systems developed at the Los Alamos National Laboratory (LANL). It consists of 42 {sup 3}He detectors to measure gross neutrons (singles), coincidence neutrons (doubles), higher order multiplicity counting (triples, quadruples, etc.). It can effectively operate in both active and passive neutron interrogation modes. It can utilize AmLi, AmBe, or {sup 252}Cf active interrogation neutron sources. It is used to verify declared fissile mass ({sup 235}U or {sup 239}Pu) present in SNM. Objectives: Calibrate HPGe and AWCC for lightly irradiated (with enough {sup 137}Cs gamma background) ∼93% enriched HEU fuels; Verify fissile mass ({sup 235}U +{sup 239}Pu) content using AWCC and HPGe; Model and benchmark AWCC in MCNP6. Neutron coincidence and multiplicity counting: Two or more neutrons are coincident if they are detected by the system within the specified gate window; In AWCC: Gate window is 128 μsec; Induced fission in fissile material such as {sup 235}U and {sup 239}Pu - emission of time correlated neutrons - Singles, Doubles, Triples, or Quadruples; No induced fission in non-fissile materials- no correlated neutrons - only singles. SNM can be verified with high accuracy and precision using gamma and neutron NDA instruments such as HPGe and AWCC. Interaction with thermal neutrons. Non-fissile atoms - do not emit correlated neutrons. Fissile atoms - emit correlated neutrons during induced fission events. The time correlated neutrons can be detected by using coincidence or multiplicity counters such as AWCC. Likewise, {sup 235}U produces 186 keV gamma peak that can be measured by a HPGe gamma detector. Counts under 186 keV gamma peak provide information about {sup 235}U content. Combining AWCC and HPGe results can provide better understanding of special nuclear material under investigation.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗
DOE OSTI2022

Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation

We present a classically tractable model that leads to optimized low-depth quantum circuits leveraging separable-pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms. The associated wave functions can be represented with linear memory requirement, which allows classical optimization of the circuits and naturally defines a minimum benchmark for quantum algorithms. In this work we employ directly determined pair-natural orbitals within a basis-set-free approach. This leads to accurate representation of the one- and many-body parts for weakly correlated systems and we explicitly illustrate how the model can be integrated into other quantum algorithms for stronger correlated systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

β decay of Ba 141

The β-decay strength function of nuclides produced in fission is important as it dictates the distribution of decay energy between electrons, neutrinos, and γ rays and so is critical for calculating decay heat in reactors and for estimating the reactor antineutrino spectrum. Several experimental techniques are available to determine this strength function, including electron spectroscopy, γ-ray calorimetry (TAGS spectroscopy), and detailed, high-resolution spectroscopy with modern large high-purity germanium arrays. This work investigates the decay of the well-known and strongly produced fission fragment 141 Ba. A beam of 141 Cs was implanted at the target position of the Gammasphere and the subsequent decay of the daughter 141 Ba was studied. Extensive decay spectroscopy was possible up to the decay Q value of 3.197(7) MeV, including a significant extension of the level scheme and detailed angular correlation measurements for all levels with greater than 0.25% β feeding. The distribution of the β-decay strength was then inferred and compared to previous calorimetric studies. In conclusion, the agreement was excellent and provides a benchmark for comparing strength function methods and data for a more detailed understanding of the structure of 141 La.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

Stagnation-point heat-transfer rate predictions at aeroassist flight conditions

The results are presented for the stagnation-point heat-transfer rates used in the design process of the Aeroassist Flight Experiment (AFE) vehicle over its entire aeropass trajectory. The prediction methods used in this investigation demonstrate the application of computational fluid dynamics (CFD) techniques to a wide range of flight conditions and their usefulness in a design process. The heating rates were computed by a viscous-shock-layer (VSL) code at the lower altitudes and by a Navier-Stokes (N-S) code for the higher altitude cases. For both methods, finite-rate chemically reacting gas was considered, and a temperature-dependent wall-catalysis model was used. The wall temperature for each case was assumed to be radiative equilibrium temperature, based on total heating. The radiative heating was estimated by using a correlation equation. Wall slip was included in the N-S calculation method, and this method implicitly accounts for shock slip. The N-S/VSL combination of projection methods was established by comparison with the published benchmark flow-field code LAURA results at lower altitudes, and the direct simulation Monte Carlo results at higher altitude cases. To obtain the design heating rate over the entire forward face of the vehicle, a boundary-layer method (BLIMP code) that employs reacting chemistry and surface catalysis was used. The ratio of the VSL or N-S method prediction to that obtained from the boundary-layer method code at the stagnation point is used to define an adjustment factor, which accounts for the errors involved in using the boundary-layer method.

Gupta, Roop N.↗
NASA NTRS2011

A Critical Examination of Spatial Biases Between MODIS and MISR Aerosol Products - Application for Potential AERONET Deployment

AErosol RObotic NETwork (AERONET) data are the primary benchmark for evaluating satellite-retrieved aerosol properties. However, despite its extensive coverage, the representativeness of the AERONET data is rarely discussed. Indeed, many studies have shown that satellite retrieval biases have a significant degree of spatial correlation that may be problematic for higher-level processes or inverse-emissions-modeling studies. To consider these issues and evaluate relative performance in regions of few surface observations, cross-comparisons between the Aerosol Optical Depth (AOD) products of operational MODIS Collection 5.1 Dark Target (DT) and operational MODIS Collection 5.1 Deep Blue (DB) with MISR version 22 were conducted. Through such comparisons, we can observe coherent spatial features of the AOD bias while side-stepping the full analysis required for determining when or where either retrieval is more correct. We identify regions where MODIS to MISR AOD ratios were found to be above 1.4 and below 0.7. Regions where lower boundary condition uncertainty is likely to be a dominant factor include portions of Western North America, the Andes mountains, Saharan Africa, the Arabian Peninsula, and Central Asia. Similarly, microphysical biases may be an issue in South America, and specific parts of Southern Africa, India Asia, East Asia, and Indonesia. These results help identify high-priority locations for possible future deployments of both in situ and ground based remote sensing measurements. The Supplement includes a km1 file.

Shi, Y.↗
DOE OSTI2023

Seasonal forecasting skill for the High Mountain Asia region in the Goddard Earth Observing System

Seasonal variability of the global hydrologic cycle directly impacts human activities, including hazard assessment and mitigation, agricultural decisions, and water resources management. This is particularly true across the High Mountain Asia (HMA) region, where availability of water resources can change depending on local seasonality of the hydrologic cycle. Forecasting the atmospheric states and surface conditions, including hydrometeorologically relevant variables, at subseasonal-to-seasonal (S2S) lead times of weeks to months is an area of active research and development. NASA's Goddard Earth Observing System (GEOS) S2S prediction system has been developed with this research goal in mind. Here, we benchmark the forecast skill of GEOS-S2S (version 2) hydrometeorological forecasts at 1–3-month lead times in the HMA region, including a portion of the Indian subcontinent, during the retrospective forecast period, 1981–2016. To assess forecast skill, we evaluate 2 m air temperature, total precipitation, fractional snow cover, snow water equivalent, surface soil moisture, and terrestrial water storage forecasts against the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) and independent reanalysis data, satellite observations, and data fusion products. Anomaly correlation is highest when the forecasts are evaluated against MERRA-2 and particularly in variables with long memory in the climate system, likely due to the similar initial conditions and model architecture used in GEOS-S2S and MERRA-2. When compared to MERRA-2, results for the 1-month forecast skill range from an anomaly correlation of R anom =0.18 for precipitation to R anom =0.62 for soil moisture. Anomaly correlations are consistently lower when forecasts are evaluated against independent observations; results for the 1-month forecast skill range from R anom =0.13 for snow water equivalent to R anom =0.24 for fractional snow cover. We find that, generally, hydrometeorological forecast skill is dependent on the forecast lead time, the memory of the variable within the physical system, and the validation dataset used. Overall, these results benchmark the GEOS-S2S system's ability to forecast HMA hydrometeorology.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Response of vibrational properties and thermal conductivity of perovskites to pressure

We study the response of SrTiO 3 and KTaO 3 's vibrational properties and thermal conductivity to pressurization. Our goal is to improve the understanding of the relationship between crystal structure, vibrational dynamics, and thermal conductivity in perovskites. We measure the thermal conductivity of SrTiO 3 and KTaO 3 up to 28 GPa by time-domain thermoreflectance. We also perform Raman scattering and stimulated Brillouin scattering measurements of SrTiO 3 and KTaO 3 to characterize changes in vibrational dynamics with pressure. The thermal conductivity of SrTiO 3 increases under pressure with a slope comparable to that of other perovskites whose thermal conductivity has been measured versus pressure. Alternatively, the thermal conductivity of KTaO 3 has a stronger pressure dependence than that of other materials with similar crystal structure. We correlate pressure-induced changes in Raman and Brillouin spectra with pressure-induced changes in thermal conductivity. We show that pressure-induced changes in phonon lifetimes dominate the pressure dependence of thermal conductivity. This study provides benchmark knowledge of why depends on pressure and improves understanding of structure/thermal-property relationships.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster perturbation theory (CPT) is a computationally economic method commonly used to estimate the momentum- and energy-resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. Finally, we benchmark the method with the one-dimensional Fermi-Hubbard model by comparing with known results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Ground-state properties of the Hubbard model in one and two dimensions from the Gutzwiller conjugate gradient minimization theory

We introduce Gutzwiller conjugate gradient minimization (GCGM) theory, an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. GCGM uses the Gutzwiller wave function but does not use the commonly adopted Gutzwiller approximation (GA), which is a major source of inaccuracy. Instead, the theory uses an approximation that is based on the occupation probability of the on-site configurations, rather than approximations that decouple the site-site correlations as used in the GA. We test the theory in the one-dimensional and two-dimensional Hubbard models at various electron densities and find that GCGM reproduces energies and double occupancies in reasonable agreement with benchmark data at a very small computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Robust historical evapotranspiration trends across climate regimes

Evapotranspiration (ET) links the hydrological, energy and carbon cycles on the land surface. Quantifying ET and its spatio-temporal changes is also key to understanding climate extremes such as droughts, heatwaves and flooding. Regional ET estimates require reliable observation-based gridded ET datasets, and while many have been developed using physically based, empirically based and hybrid techniques, their efficacy, and particularly the efficacy of their uncertainty estimates, is difficult to verify. In this work, we extend the methodology used in Hobeichi et al. (2018) to derive two new versions of the Derived Optimal Linear Combination Evapotranspiration (DOLCE) product, with observationally constrained spatio-temporally varying uncertainty estimates, higher spatial resolution, more constituent products and extended temporal coverage (1980–2018). After demonstrating the efficacy of these uncertainty estimates with out-of-sample testing, we derive novel ET climatology clusters for the land surface, based on the magnitude and variability of ET at each location on land. The new clusters include three wet and three dry regimes and provide an approximation of Köppen–Geiger climate classes. The verified uncertainty estimates and extended time period then allow us to examine the robustness of historical trends spatially and in each of these six ET climatology clusters. We find that despite robust decreasing ET trends in some regions these do not correlate with behavioural ET clusters. Each cluster, and the majority of the Earth's surface, shows clear robust increases in ET over the recent historical period. The new datasets DOLCE V2.1 and DOLCE V3 can be used for benchmarking global ET estimates and for examining ET trends respectively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Additively manufactured β-Ti5553 with laser powder bed fusion: Microstructures and mechanical properties of bulk and lattice parts

Ti5553 (Ti-5Al-5Mo-5V-3Cr wt%) is a titanium alloy widely used for its high strength-to-weight ratio and good formability at elevated temperatures. Unlike Ti-6Al-4V, Ti5553 does not undergo martensitic transformation, preventing cracking of brittle martensite upon rapid cooling. This makes it a strong candidate for additive manufacturing (AM), particularly laser powder bed fusion (L-PBF). L-PBF offers the unique opportunity to make fine lattice structures to reduce component weight. Despite the growing field of AM, there have been limited studies on L-PBF Ti5553 lattices and how their properties differ from the bulk. Here the present work addresses this knowledge gap by investigating microstructures and properties of L-PBF bulk and lattice parts and the effect of post L-PBF heat treatments. Electron microscopy and mechanical testing show that the high dislocation density formed during L-PBF increases bulk part’s yield strength by approximately 100 MPa compared to the conventional alloy. Digital image correlation during compression testing of octet truss lattices reveals a layer-by-layer failure mode. Compared to the bulk, the lattice contains copious ω nanoprecipitation, weaker <001> texture, smaller average grain sizes, and larger content of high-angle grain boundaries. These features elicit differences in Taylor factor distributions for the lattice depending on load direction, underlining challenges in predicting lattice mechanical response based on bulk properties. By examining the processing-structure-property relationships in the bulk and lattice, the present results delineate their microstructural and mechanical differences and establish a benchmark for the future design applications of L-PBF Ti5553.

36 MATERIALS SCIENCE↗
NASA NTRS2023

Seasonal Forecasting Skill for the High Mountain Asia Region in the Goddard Earth Observing System

Seasonal variability of the global hydrologic cycle directly impacts human activities, including hazard assessment and mitigation, agricultural decisions, and water resources management. This is particularly true across the High Mountain Asia (HMA) region, where availability of water resources can change depending on local seasonality of the hydrologic cycle. Forecasting the atmospheric states and surface conditions, including hydrometeorological relevant variables, at subseasonal-to-seasonal (S2S) lead times of weeks-to-months is an area of active research and development. NASA’s 15 Goddard Earth Observing System (GEOS) S2S prediction system has been developed with this research goal in mind. Here, we benchmark the forecast skill of GEOS-S2S (version 2) hydrometeorological forecasts at 1-3 month lead times in the HMA region, including a portion of the Indian Subcontinent, during the retrospective forecast period, 1981-2016. To assess forecast skill, we evaluate 2-m air temperature, total precipitation, fractional snow cover, snow water equivalent, surface soil moisture, and terrestrial water storage forecasts against the Modern-Era Retrospective analysis for Research and 20 Applications, Version 2 (MERRA-2) and independent reanalysis data, satellite observations, and data fusion products. Anomaly correlation is highest when the forecasts are evaluated against MERRA-2 and particularly in variables with long memory in the climate system, likely due to similar initial conditions and model architecture used in GEOS-S2S and MERRA-2. When compared to MERRA-2, results for the 1-month forecast skill range from anomaly correlation of R anom =0.18 for precipitation to R anom =0.62 for soil moisture. Anomaly correlations are consistently lower when forecasts are 25 evaluated against independent observations; results for the 1-month forecast skill range from R anom =0.13 for snow water equivalent to R anom =0.24 for fractional snow cover. We find that, generally, hydrometeorological forecast skill is dependent on the forecast lead time, the memory of the variable within the physical system, and the validation dataset used. Overall, these results benchmark the GEOS-S2S system’s ability to forecast HMA hydrometeorology.

GEOS↗
DOE OSTI2022

Small angle scattering of diblock copolymers profiled by machine learning

We outline a machine learning strategy for quantitively determining the conformation of AB-type diblock copolymers with excluded volume effects using small angle scattering. Complemented by computer simulations, a correlation matrix connecting conformations of different copolymers according to their scattering features is established on the mathematical framework of a Gaussian process, a multivariate extension of the familiar univariate Gaussian distribution. We show that the relevant conformational characteristics of copolymers can be probabilistically inferred from their coherent scattering cross sections without any restriction imposed by model assumptions. This work not only facilitates the quantitative structural analysis of copolymer solutions but also provides the reliable benchmarking for the related theoretical development of scattering functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

25-Pin metallic fuel performance benchmark case based on the EBR-II X430 experiments series

A metallic fuel benchmark case was developed for the fuel performance code BISON based on 25 uranium-zirconium and uranium-plutonium-zirconium pins of the Experimental Breeder Reactor II X430 experiment series. Results of the benchmarks were compared with measurements and calculations made at the time of the experiment as well as subsequent measurements reported in 2019. The comparisons were used to quantify the accuracy of the BISON predictions and to identify patterns in the BISON differences.BISON predicted burnup, plenum pressure, and fission gas release fractions accurately. BISON temperature predictions were somewhat cooler than the temperatures determined at the time of the experiment but appeared to be reasonably accurate considering uncertainties in the legacy temperature calculations, uncertainties in the legacy linear heat rate calculations, and the high sensitivities of the BISON-predicted temperatures to BISON inputs. Fuel axial elongation predictions had errors correlated to fuel composition; BISON tended to underpredict the elongation of binary fuels and overpredict the elongation of ternary fuels. BISON cladding radial dilation predictions were also significantly lower than legacy PIE measurements.Recommendations were made to improve the BISON fuel gaseous swelling model to account for fuel composition, to add additional capabilities to the coolant channel temperature model to ease benchmark development, and to continue developing benchmark cases based on a wide range of experiments in several reactors. Once a wide array of benchmarks is developed, an attempt can be made to enhance or calibrate BISON models to improve the cladding dilation predictions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

A comparison between the one- and two-step spin-orbit coupling approaches based on the ab initio Density Matrix Renormalization Group

The efficient and reliable treatment of both spin-orbit coupling (SOC) and electron correlation is essential for understanding f-element chemistry. Here, we analyze two approaches to the problem, the one-step approach where both effects are treated simultaneously, and the two-step state interaction approach. We report an implementation of the ab initio density matrix renormalization group(DMRG) with a one-step treatment of the SOC effect which can be compared to prior two-step treatments on an equal footing. Using a dysprosium octahedral complex and bridged dimer as benchmark systems, we identify characteristics of problems where the one-step approach is beneficial for obtaining the low-energy spectrum.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ~10 9 two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. Furthermore, this work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗